A tree diagram
shows all the possible outcomes of an event and their probabilities
We can find the probability of one event or
A Single Coin Toss
A single coin toss can be shown on a tree diagram.
The probability of each event can be read from each branch:
The probability of getting Heads is 1⁄2.
The probability of getting Tails is 1⁄2.
Imagine we wanted to find the probability of getting Heads or Tails
The probability of Heads or Tails
is found by adding
1⁄2 + 1⁄2 = 1
How to Find the Probability of an Event or Another Event on a Tree Diagram
The addition rule can be used for more complicated tree diagrams.
The tree diagram below is for a double coin toss.
What is the probability of both tosses landing the same side up?
To find the probability of an event or
another event, add across
Find the event given in the question.
The event is the coin landing the same side up on both tosses. There are two ways this can happen:
Heads and Heads
Tails and Tails
We are finding the probability of Heads and Heads or Tails and Tails
. These are the top branches and the bottom branches of the tree diagram.
Use the multiplication rule
to find the probabilities of the outcomes.
the probabilities along
For Heads and Heads
P(Heads and Heads) = 1⁄2 × 1⁄2 = 1⁄4
For Tails and Tails
P(Tails and Tails) = 1⁄2 × 1⁄2 = 1⁄4
Add the probabilities for these outcomes.
1⁄4 × 1⁄4 = 2⁄4
the fraction if possible. (The fraction in our example is already as simple as possible).
Simplify the fraction by dividing
the top and bottom numbers by their greatest common factor
(which is 2).
2 ÷ 2 = 1
4 ÷ 2 = 2
The probability of getting Heads and Heads or Tails and Tails
We can also express this as a number (0.5) or a percentage
The slider below another real example of using the addition rule on a tree diagram.
What Is Probability?
A probability is a measure of how likely (how probable
) an event is to happen.
A probability is expressed as a number between 0 (impossible) and 1 (certain).
The formula for finding a probability is shown below:
A Useful Check
There is a useful way to check that the probabilities on a tree diagram are all correct.
The probabilities of each final outcome add up to 1: